Response Surface Methodology（英文）.pptVIP

Response Surface Methodology What is Response Surface Methodology (RSM) Response Surface Methodology (RSM) is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several quantifiable variables (or factors), with the objective of optimizing the response. Response Surface The yield of a process (Y) was determined to be influenced by the amount of nitrogen (X1) and phosphoric acid (X2), i.e. Y = ?(X1, X2) + ? where ? is the noise or error observed in the response. If we denote the expected response by E(Y) = ?(X1, X2) = ? then the surface represented by ? = ?(X1, X2) is called a response surface. Response Surface Plots Response Surface Plots show how a response variable relates to two quantifiable factors based on a model equation. Response Surface Designs Designs for fitting response surfaces are called response surface designs. When choosing a design identify the number of control factors under investigation determine the limiting number of experimental runs ensure adequate coverage of the region of interest determine the impact of economics – cost, time, availability, etc Response Surface Methodology – Why? Response Surface Methods are used to examine the relationship between one or more responses and a set of quantifiable factors to search for the setting of critical control factors that would optimize the response when curvature in the response surface is suspected Response Surface Methodology – When? Response Surface Methods may be employed to find factor settings that produce the “best” response find factor settings in which operating or process specifications are satisfied identify new operating conditions that would produce the required improvement in product quality model a relationship between the control factors and the response Response Surface Functions Response Surface Functions RSM seeks to identify the rela